Two wine merchants enter Paris, one of them with 64 casks of wine, the other with 20. Since they have not enough money to pay the custom duties, the first pays 5 casks of wine and 40 francs, and the second pays 2 casks of wine and receives 40 francs in change. What is the price of each cask of wine and the duty on it?

Determine how much do individual firms produce : Industry X has a market demand curve given by the equation P = 100 - Q/100, where P is the market price, and Q is industry-wide output.100 perfectly competitive firms currently operate in industry X. Each of these firms has a total cost function g.. |

What is the probability that wait at least an additional min : what is the probability that you will have to wait longer than 10 minutes? if at 10:15 the bus has not yet arrived, what is the probability that you will have to wait at least an additional 10 minutes? |

Explain a firefighter aim a fire hose : A firefighter aim a fire hose from 4 feet above the ground at a window that is 26 feet above the ground. The equation h=-0.01d^2+1.06d+4 models the path of the water when h equals height in feet |

How much will each firm produce in the equilibrium : A competitive industry currently consists of N= 10 identical firms. An individual firm's total cost function is given by TC = 0.5q2 + 200. Market demand is given by Q = 3000-5P. In the short run, how much will each firm produce in the equilibrium |

State two wine merchants enter paris : Two wine merchants enter Paris, one of them with 64 casks of wine, the other with 20. Since they have not enough money to pay the custom duties, the first pays 5 casks of wine and 40 francs |

Explain the changes in the corn industry in tap : The small island of Tap, inhabited by the Tapese people, produces a single variety of corn. At the present time, each farmer produces his or her own corn, harvests it and carries it to the market for sale. On any market day in Tap, you will find m.. |

State what dimensions of the silo will use : The silo will be cylindrical in shape and have a flat top. The floor of the silo will be earth. What dimensions of the silo will use the least material for construction? |

Calculate tonys average cost curves atc and afc : Tony owns a fancy Italian restaurant, Tony's Trattoria. He uses only the finest ingredients and hires the best chefs in the country. Suppose Tony's total cost function is given by the following relationship: TC =100 +10Q +Q^2 , where Q is the numb.. |

Explain a refrigerator where the temperature is a constant : Use Newton's Law of Cooling in the following example. A thermometer reading 72 degrees Fahrenheit is placed into a refrigerator where the temperature is a constant 38 degrees Fahrenheit. |

## What is the minimum value for the sum of these two forcesForces of 4 N and 6 N act on an object. What is the minimum value for the sum of these two forces? |

## Find the speed of the wind and the speed of the planeFlying with the wind a plane went 154 mph. Flying into the same wind the plane only went 124 mph. Find the speed of the wind and the speed of the plane in still air. |

## Volume of cubes and area of triangleA large cube is 2 feet on each edge. How many cubes - one inch on each edge- will it take to fill the large cube? If the base of a triangle is increased by 20% and the altitude to that base is decreased by 40% then by what percent is the area chang.. |

## Show that the fourier transform of the complex exponentialshow that the fourier transform of the complex exponential signal e^(+jwt) is one peak in the positive spectrum at the angular frequency w use the inverse FT formula. |

## Geometric application problemApplication Problem 1G (Geometric application- See Appendix A in your textbook for formulas of geometric figures) |

## Find the midpoint of the midsegment of the trapezoidfind the midpoint of the midsegment of the trapezoid if A=(4r, 4s), B=(4t, 4s) and C=(4u, 0) |

## Approximate the area bounded by f(x) and the x axisf(x)= the square root of x^2+1 and [0,4] . Use the midpoint rule with 4 rectangles to approximate the area bounded by f(x) and the x axis. |

## What is the probability that a randomly selected bikeWhat is the probability that a randomly selected bike that did not pass inspection came from assembly line B? |

## Question regarding system of inequalitiesGive a real-life example of a situation in which you would use a system of inequalities, and for which the solution must be in the first quadrant. |

## What should the dimensions of the page beA rectangular page is to contain square inches of printable area. The margins at the top and bottom of the page are each inch, one side margin is inch, and the other side margin is inches. What should the dimensions of the page be so that the leas.. |

## What is the length of the belt to the nearest mmthree wheels wrapped tightly together with a belt, each wheel has a radius of 10 cm. What is the length of the belt to the nearest mm? |

## Find the riemann sum(a) Find the Riemann sum for f(x) = x - 4 sin 2x, 0 x 3, with six terms, taking the sample points to be right endpoints. (Give your answer correct to six decimal places.) |

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